On parametric bootstrap methods for small area prediction
On parametric bootstrap methods for small area prediction
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DOI：
10.1111/j.1467-9868.2006.00541.x
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发表时间：
2006-01-01
影响因子：
5.8
通讯作者：
Maiti, T
中科院分区：
文献类型：
--
作者：
Hall, P;Maiti, T
小区域预测的应用范围特别广泛，例如在政策制定决策中，这意味着该主题近年来受到了广泛关注。估计均方预测误差、纠正估计量的偏差以及构建预测区间的问题已经被许多工作人员解决，尽管现有的方法仍然局限于狭窄的模型范围。为了克服这一困难，我们开发了新的基于引导程序的方法，该方法适用于非常一般的设置，用于构建均方误差的偏差校正估计器和计算预测区域。与主要基于泰勒展开的现有技术不同，我们的偏差校正均方误差估计器不需要分析计算。它们还具有非负的性质。如果采用双引导方法，我们的预测区间具有很高的覆盖精度，O(n(-3))，其中 n 是区域数量。这些技术不依赖于小区域估计量的形式，并且适用于一般的两级小区域模型，其中任一级别的变量可以是离散的或连续的，特别是可以是非正态的。最重要的是，新方法简单且易于应用。
The particularly wide range of applications of small area prediction, e.g. in policy making decisions, has meant that this topic has received substantial attention in recent years. The problems of estimating mean-squared predictive error, of correcting that estimator for bias and of constructing prediction intervals have been addressed by various workers, although existing methodology is still restricted to a narrow range of models. To overcome this difficulty we develop new, bootstrap-based methods, which are applicable in very general settings, for constructing bias-corrected estimators of mean-squared error and for computing prediction regions. Unlike existing techniques, which are based largely on Taylor expansions, our bias-corrected mean-squared error estimators do not require analytical calculation. They also have the property that they are non-negative. Our prediction intervals have a high degree of coverage accuracy, O(n(-3)), where n is the number of areas, if double-bootstrap methods are employed. The techniques do not depend on the form of the small area estimator and are applicable to general two-level, small area models, where the variables at either level can be discrete or continuous and, in particular, can be non-normal. Most importantly, the new methods are simple and easy to apply.